The Universe as a Domain Wall

TL;DR

This paper derives a five-dimensional supergravity theory from heterotic string compactification, finds a three-brane domain wall solution, and connects it to four-dimensional physics with branes as our universe.

Contribution

It explicitly constructs a gauged five-dimensional supergravity theory with boundaries from heterotic string theory and finds an exact three-brane domain wall solution relevant for four-dimensional models.

Findings

Derived the effective 5D supergravity from heterotic string compactification.

Found an exact three-brane domain wall solution matching Witten's background.

Connected the domain wall solution to four-dimensional physics with branes as our universe.

Abstract

It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of N=1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a "non-zero mode" of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten's "deformed" Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the four-dimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane worldvolume.